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Each week a certain salesman is paid a fixed amount equal to [#permalink]

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21 Jul 2012, 11:30

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Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?

(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week. (2) The salesman's sales last week totaled $5,000.

OG says answer is D. I am confused with their explanation for the statement 1. profit = .10Sales and profit = 300 + 0.05(S-1000). And thats how they solve both the equations.

What i don't understand is what if Sale for that week is 500 or less than 1000. He doesn't earn any commission and there isn't any statement which says that he has a penalty. So ideally it should be only 300. But above with above equation he will earn less than 300. Can someone please explain !!!

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?

(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week. (2) The salesman's sales last week totaled $5,000.

OG says answer is D. I am confused with their explanation for the statement 1. profit = .10Sales and profit = 300 + 0.05(S-1000). And thats how they solve both the equations.

What i don't understand is what if Sale for that week is 500 or less than 1000. He doesn't earn any commission and there isn't any statement which says that he has a penalty. So ideally it should be only 300. But above with above equation he will earn less than 300. Can someone please explain !!!

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?

Say S is the amount of his sales that week, then:

If \(S\leq{1,000}\), salesman's profit is \($300\); If \(S>1,000\), salesman's profit is \($300+(S-1,000)*0.05\).

So, no penalties there, just two cases for the profit: if \(S\leq{1,000}\) then the profit is simply $300 and if \(S>1,000\), then the profit is \($300+(S-1,000)*0.05\).

(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week. Given: \(profit=0.1*S\). It's clear that S must be greater than $1,000, so we have that \($300+(S-1,000)*0.05=0.1S\). We can calculate S, hence calculate the profit. Sufficient.

(2) The salesman's sales last week totaled $5,000. Directly gives the value of S, hence calculate the profit. Sufficient.

Kindly advise what if the sales were less than USD 1000 , lets say the sales of a last week were USD 800. How to check sufficiency of A then ??

Statements 1 and 2 in DS never contradict each other.

For explanation sake how to confirm statement 1 without any help from statement 2. Case being sales less than USD 1000. I might be missing something but I would certainly like to know how to make statement 1 sufficient without any help from statement 2.

Re: Each week a certain salesman is made a fixed amount equal to [#permalink]

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13 Apr 2013, 09:35

2

This post received KUDOS

For your what if scenario the answer is as follows -

Amount from the commission would be 0 and salesman would have made last week only $300. Typically in GMAT you take the question and statements as facts.

//kudos please, if the above explanation is good.
_________________

For explanation sake how to confirm statement 1 without any help from statement 2. Case being sales less than USD 1000. I might be missing something but I would certainly like to know how to make statement 1 sufficient without any help from statement 2.

Maybe I don't understand what you are trying to say...

However from the text we can create the formula for the tot amount \(x=300+5%(Sales-1000)\) Lets esamine statement 1:the total amount the salesman was paid last week is equal to 10 percent of the amount of these sales last week \(x=10%Sales\) and we don't know nothing else, I haven't read stetement 2 and I cannot hypothesize the case with Sales<1000$ (there is no reason to do so, I have to take into consideration what the text says and nothing else). \(300+0.05(S-1000)=0.1S\) do some math and obtain the tot sales \(S = 5000\) Sufficient. I haven't read st 2 and I am able to answer, your "Case being sales less than USD 1000" is a consideration that goes against the info in the text. When you answer a question stick to the text: don't make any hypothesis that could compromize the answer.

Hope that I have answered your question, let me know
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: Each week a certain salesman is paid a fixed amount equal to [#permalink]

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23 Oct 2015, 22:04

In a data sufficiency question is it necessary for both the statements to return the same unique value ? I was going through another post of the same question , in which PiyushK has provided a new statement :modified statement 1 : Sales man income was 50% of his total sale. The below is the link to the question- each-week-a-certain-salesman-is-paid-a-fixed-amount-equal-to-6616.html

Experts please help!!
_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long +1 Kudos if you find this post helpful

In a data sufficiency question is it necessary for both the statements to return the same unique value ? I was going through another post of the same question , in which PiyushK has provided a new statement :modified statement 1 : Sales man income was 50% of his total sale. The below is the link to the question- each-week-a-certain-salesman-is-paid-a-fixed-amount-equal-to-6616.html

Experts please help!!

Yes, both the statements are a part of the same question. One cannot return that x is 2 if the other says that x is 7. In one question, x can take only one unique value. So if both statements are giving you a unique value, the value will be the same. If it isn't, it means you have made a mistake somewhere. Of course, it is possible that one statement gives you a bunch of possible values for x and the other gives you a unique value but obviously, the unique value would be a part of the bunch of values given by the other statement.
_________________

Re: Each week a certain salesman is paid a fixed amount equal to [#permalink]

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25 Oct 2015, 22:38

VeritasPrepKarishma wrote:

skywalker18 wrote:

In a data sufficiency question is it necessary for both the statements to return the same unique value ? I was going through another post of the same question , in which PiyushK has provided a new statement :modified statement 1 : Sales man income was 50% of his total sale. The below is the link to the question- each-week-a-certain-salesman-is-paid-a-fixed-amount-equal-to-6616.html

Experts please help!!

Yes, both the statements are a part of the same question. One cannot return that x is 2 if the other says that x is 7. In one question, x can take only one unique value. So if both statements are giving you a unique value, the value will be the same. If it isn't, it means you have made a mistake somewhere. Of course, it is possible that one statement gives you a bunch of possible values for x and the other gives you a unique value but obviously, the unique value would be a part of the bunch of values given by the other statement.

"Of course, it is possible that one statement gives you a bunch of possible values for x and the other gives you a unique value but obviously, the unique value would be a part of the bunch of values given by the other statement" As per this if statement 1 returns 2 values of x - a and b and statement 2 returns a single value of x = a Then we can conclude that x=a is the solution. Then our answer choice will be C right ? In other words x can take a value which is intersection of result set 1 and 2 . And if the intersection of the 2 result sets is null then we will have option E .
_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long +1 Kudos if you find this post helpful

In a data sufficiency question is it necessary for both the statements to return the same unique value ? I was going through another post of the same question , in which PiyushK has provided a new statement :modified statement 1 : Sales man income was 50% of his total sale. The below is the link to the question- each-week-a-certain-salesman-is-paid-a-fixed-amount-equal-to-6616.html

Experts please help!!

Yes, both the statements are a part of the same question. One cannot return that x is 2 if the other says that x is 7. In one question, x can take only one unique value. So if both statements are giving you a unique value, the value will be the same. If it isn't, it means you have made a mistake somewhere. Of course, it is possible that one statement gives you a bunch of possible values for x and the other gives you a unique value but obviously, the unique value would be a part of the bunch of values given by the other statement.

"Of course, it is possible that one statement gives you a bunch of possible values for x and the other gives you a unique value but obviously, the unique value would be a part of the bunch of values given by the other statement" As per this if statement 1 returns 2 values of x - a and b and statement 2 returns a single value of x = a Then we can conclude that x=a is the solution. Then our answer choice will be C right ? In other words x can take a value which is intersection of result set 1 and 2 . And if the intersection of the 2 result sets is null then we will have option E .

So this is why DS questions are tricky. Think about it:

if statement 1 returns 2 values of x - a and b and statement 2 returns a single value of x = a Then we can conclude that x=a is the solution.

Correct!

Then our answer choice will be C right ?

Wrong! The answer will be (B) in that case (assuming statement II tells you that x = a). If one statement gives you a unique value for x, it alone is sufficient. We don't need the more generic other statement which gives us multiple values for x.

When will the answer be (C)? When statement 1 gives x = a or b and statement 2 gives x = a or c Now you need both statements to see that x can take only one value "a", if it has to satisfy both statements.

And if the intersection of the 2 result sets is null then we will have option E . If intersection of the two result sets in null, it is a wrong DS question since there has to be at least one common value (your original question). The answer will be (E) when the two sets have multiple values in the overlap. When statement 1 gives x = a or b or c and statement 2 gives x = a or c. Using both statements, we can say that x is either a or c. But we do not know which. So answer is (E)
_________________

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?

(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week. (2) The salesman's sales last week totaled $5,000.

If we modify the question, making sales' payment:p, sales amount:s, p=300+(s-1000)5%. There are 2 variables (p,s) and an equation, so we need one more equation when 2 are actually given from the 2 conditions; there is high chance (D) will be our answer. From condition 1, it is sufficient as p=0.1s and condition 2 is also sufficient in s=5000. The answer therefore becomes (D)

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?

(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week. (2) The salesman's sales last week totaled $5,000.

Solution:

We are given that a salesman is paid $300, plus a commission equal to 5 percent of the amount of his sales over $1,000. If we set variable T as the total amount of his sales and A as the amount he earned last week, we can create the following equation:

A = 300 + 0.05(T – 1,000)

We need to determine the value of A.

Statement One Alone:

The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.

Using the information we can create the following equation:

A = 0.1T

Since A = 0.1T, we can substitute 0.1T for A in the equation A = 300 + 0.05(T – 1,000).

0.1T = 300 + 0.05T – 50

0.05T = 250

5T = 25,000

T = 5,000

Since we have a value for T, we can determine A.

A = 300 + 0.05(5,000 – 1,000)

A = 300 + 0.05(4,000)

A = 300 + 200

A = 500

Statement one is sufficient to answer the question. We can eliminate answer choice B, C, and E.

Statement Two Alone:

The salesman's sales last week totaled $5,000.

Once again, since we have a value for T, we can determine the value of A. Statement two is sufficient to answer the question.

The answer is D.
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: Each week a certain salesman is paid a fixed amount equal to [#permalink]

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08 Aug 2016, 22:20

JeffTargetTestPrep wrote:

summer101 wrote:

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?

(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week. (2) The salesman's sales last week totaled $5,000.

Solution:

We are given that a salesman is paid $300, plus a commission equal to 5 percent of the amount of his sales over $1,000. If we set variable T as the total amount of his sales and A as the amount he earned last week, we can create the following equation:

A = 300 + 0.05(T – 1,000)

We need to determine the value of A.

Statement One Alone:

The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.

Using the information we can create the following equation:

A = 0.1T

Since A = 0.1T, we can substitute 0.1T for A in the equation A = 300 + 0.05(T – 1,000).

0.1T = 300 + 0.05T – 50

0.05T = 250

5T = 25,000

T = 5,000

Since we have a value for T, we can determine A.

A = 300 + 0.05(5,000 – 1,000)

A = 300 + 0.05(4,000)

A = 300 + 200

A = 500

Statement one is sufficient to answer the question. We can eliminate answer choice B, C, and E.

Statement Two Alone:

The salesman's sales last week totaled $5,000.

Once again, since we have a value for T, we can determine the value of A. Statement two is sufficient to answer the question.

The answer is D.

awesome explanation. This structure again emphasis to take either of the statements to other as a hint, but don't carry the information.

Total sales of 5000$ matches with the second statement with the same total sales. I have logged this question to my error list to review before the actual GMAT.

Re: Each week a certain salesman is paid a fixed amount equal to [#permalink]

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10 Feb 2017, 15:06

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?

(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week. (2) The salesman's sales last week totaled $5,000.

Clue 1: "salesman is paid a fixed amount equal to $300, plus" -> 300+

Clue 2: "a commission equal to 5 percent of the amount of his sales that week over $1,000" -> 0.05 (S - 1000) where S is the sales that week

Clue 3: "What is the total amount the salesman was paid last week" -> 300 + 0.05 (S - 1000) = ? = T

Starting with statement 2) The salesman's sales last week totaled $5,000. This means that S = 5000 : T = 300 + 0.05 (5000 - 1000) Dont bother to solve it Sufficient

Statement 1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week. T = 300 + 0.05 (S - 1000) = 0.1S -> 300 - 50 = S * 0.05 Hence S = 25000 / 5 = 5000 Dont bother to calculate anything because you found S. Since you found S you can go back to the original equation and find T

If \(S\leq{1,000}\), salesman's profit is \($300\); If \(S>1,000\), salesman's profit is \($300+(S-1,000)*0.05\).

Why we need to minus 1,000, 0.05*(S-1,000) instead of 0.05*S ?

For example Sales = 2,000, Commission = 0.05*2,000

No.

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week OVER $1,000. What is the total amount the salesman was paid last week?

So, if S = 2,000, then commission = (2,000 - 1,000)*0.05 and the profit = 300 + (2,000 - 1,000)*0.05.

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?

(1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week. (2) The salesman's sales last week totaled $5,000.

Given: Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. Let T = Total sales last week So (T - 1000) = the amount that EXCEEDS $1000 Total paycheck = $300 + 5% of (T - 1000) Or we can write: Total paycheck last week = $300 + 0.05(T - 1000)

Target question:What is the total amount the salesman was paid last week?

Statement 1: The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week. We can write: 300 + 0.05(T - 1000) = 10% of T In other words, 300 + 0.05(T - 1000) = 0.1T

ASIDE: at this point, we should recognize that we COULD solve the above equation for T, which means we COULD determine how much the salesman was paid last week. So, statement 1 is SUFFICIENT.

That said, let's solve the equation (for "fun") Take: 300 + 0.05(T - 1000) = 0.1T Simplify: 300 + 0.05T - 50 = 0.1T Simplify: 250 + 0.05T = 0.1T Subtract 0.05T from both sides: 250 = 0.05T Solve: T = 5000 If T = 5000, then: Total paycheck last week = $300 + 0.05(5000 - 1000) = 300 + 0.05(4000) = 300 + 200 = 500 So, the answer to the target question is $500 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The salesman's sales last week totaled $5,000 In other words, T = 5000 Total paycheck last week = $300 + 0.05(5000 - 1000) = 300 + 0.05(4000) = 300 + 200 = 500 So, the answer to the target question is $500 Since we can answer the target question with certainty, statement 2 is SUFFICIENT